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Ultrasonic density measurement for process control
Ultrasonic density measurement for process control J.M.
Hale
Department of Mechanical & Production Engineering, National Institute for Higher Education, Limerick, Ireland
Received
18 August
1987
A method has been devised for determining the density of a fluid by measuring the velocity and amplitude of an ultrasonic pulse passed through it. The theory of the method is presented, together with the results of an experimental verification. Keywords: ultrasonic testing; ment; process control
density
measure-
Density measurement of liquids is most easily executed by sampling, i.e. by weighing a known volume. This process is sufficient for many purposes, but is difficult to automate and by its discontinuous nature does not lend itself to continuous monitoring. It is thus unsuited to process control. A survey of commercial process instrumentation indicates that the commonest method used for continuous measurement of density is resonant vibration. There are many variations on this theme, but they all make use of the fact that the resonant frequency of a system varies with its mass. The resonant frequency of some flexible member containing a volume of the process fluid is measured and from this the fluid density is calculated. There are two problems with the resonant vibration method: the instrument normally allows only a small flow and so has to use a bleed off from the main process flow; the method is insensitive to small changes in density. By extension of the well-known expression resonant frequency = (k/m)“2/27r (where k = stiffness, m = mass), the measured parameter (frequency) is proportional to only the square root of the parameter of interest (mass or density). Thus a small change in density will produce a very small shift in resonant frequency which is difficult to measure. An alternative to resonant vibration is the use of ultrasonics. It is well known that pulse velocity and attenuation are affected by the density of the medium through which an ultrasonic pulse is propagated, the relationship depending on the type of wave. The problem is that they are also affected by other factors such as temperature. To date no simple general purpose transducer has been developed to exploit the non-invasive nature of ultrasonics to measure density. 0041-624X/88/060356-02 @ 1988 Butterworth
356
$03.00 81 Co (Publishers)
Ltd
Ultrasonics 1988 Vol 26 November
Concept
An ideal ultrasonic density transducer for process control would consist of one or two probes set radially into the wall of the pipe carrying the process fluid. This would offer no flow restriction and would measure the density of the fluid overall, not just the portion bled off into a by-pass transducer. With two probes set diametrically opposite, one would act as the transmitter and the other the receiver. Alternatively, a single probe could serve both functions with the ultrasonic pulses being reflected off the back wall of the pipe. This ideal may be realized by making use of the fact that a wave meeting an interface between two different materials is partly reflected and partly transmitted through it. The proportion transmitted is dependent only on the acoustic impedance Z of the two materials, where acoustic impedance is the product of density p and pulse velocity c. The intensity at the receiver is thus the intensity at the transmitter, less the transmission losses at the two interfaces between the probes and the fluid, less any losses in the fluid itself. Neglecting the internal losses since these are not likely to change significantly for a given fluid, if two probes of known acoustic impedance are used then changes in received intensity must be due to changes in the acoustic impedance of the process fluid. And since pulse velocity c can be measured directly from the pulse propagation time (the distance between the probes being known), the density of the fluid is the only remaining variable. Theory
-7=-t-z2
I1
z3
Transmitter
where A = pulse amplitude and Z = acoustic impedance. A2 -=-
221
Al
z,
4 -=P=_
‘4,
+z2
A,=a
222
222
z,+z,
A,
A,
.. . A,=(Z, ... A =tz, 1
Zl
since Z, = Z,
+z,
4ctz,z, +z,y +
‘25
4az,z,
4
where Z, ( = Z,) is a constant for a given pair of probes. Consider two different fluids, a reference and an unknown, of acoustic impedance Z, and Z,, respectively. For a constant input pulse amplitude A, let the received
Research note pulse amplitude A, be A, and A,, respectively, then
(21 + ZRY JZl A
4crz,z,
R
+zx)2A
4aZ,Z,
assuming the attenuation yields a quadratic in Z, z,2+
(
Equipment
(2)
x
a does not change greatly this
2z,_(Z’~Z”)2~)z,+z:_o R x
(3)
which may be solved in the usual way to yield two values of Z, provided Z, is known (see Appendix). From Z, = c,p,, using the measured pulse velocity c,, density pX may be calculated. Alternatively, let Z, = Z, + 6Z and A, = A, + &I, then Equation (2) becomes (ZI + ZR)2 A =(ZI+ZR+fiZ)2(A Z,+6z ZR R
+6A) R
neglecting small terms 6Z2 and 6Z6A, this reduces to 6Z
-_=
(4)
zR
Thus, change in acoustic impedance is directly proportional to measured change in pulse amplitude Z,=Z,+6Z
:. px =
z,+6z
(5)
and test methods
The ultrasonic pulser/detector used was a Sonatest UFS 7A. The probes were Sonatest SLlH 5-10 5 MHz immersion probes (unfocussed). The probes were set up in a tank of test fluid at a spacing of 170 mm. The pulse amplitude was measured as the height of the largest peak of the rectified signal. The pulse propagation time was measured from the detector trigger point to the received pulse break point. Conclusions The initial test of the theory outlined above gives good agreement between the ultrasonic measurement of a test fluid density and the direct measurement by weighing a measured volume. Determining either the change in acoustic impedance of the fluid or its absolute value gave a calculated density with less than 2% deviation from the true value. Of the two methods presented, the more useful is the determination of the change in acoustic impedance because it is more easily implemented on a process control computer or programmable logic controller (PLC). Calculation of absolute impedance requires the solution of a quadratic which, while not in itself difficult, contains the inherent ambiguity of two solutions, only one of which is required. Change in impedance, on the other hand, is directly proportional to change in received pulse amplitude from which density is easily calculated. Appendix
Testing The theory was tested by measuring the density of a solution of salt water (of a different concentration to that used to determine the acoustic impedance of the probes). The density obtained ultrasonically was compared with the true value obtained by weighing a known quantity of the liquid. The reference fluid used was tap water where pR = 991kgm-3,cR=1510ms-‘soZR=1.50x106kgm-2s-’. For the test fluid, c, = 1770 m s-l, A, = 9.6 mV, A, = 8.1 mV, and pX (measured directly by weighing) = 1174 kg rnm3. Solving Equation (3) gives two values for Z, of 170 x lo3 or 2.1 x lo6 kg m-2 s-l. Taking the larger value gives pX = 1200 kg m-3, a discrepancy of 2%. Alternatively, Equation (4) gives change in acoustic impedance 6Z = 550 x lo3 kg m-’ s-‘. From Equation (5), pX = 1150 kg m - 3, a discrepancy of 2%.
To determine acoustic impedance of probes. Using two reference fluids of known acoustic impedance Z, and Z,, respectively, Equation (2) becomes (Zl
+
Za)” p1
4crz,z,
A
a
+zblZA 4az,z,
b
This may be rearranged to form a quadratic in Z,
Using tap water for fluid a and salt water for fluid b c, = 1510 m s-l, p,=991kgm-3,Z,=1.50x106kgm-2s-’
A, - = 0.865 A, There is only one positive root to the quadratic: Z, = 600 x lo3 kg mm2 s-l for the probes used.
Ultrasonics 1988 Vol 26 November
357
Hale
Department of Mechanical & Production Engineering, National Institute for Higher Education, Limerick, Ireland
Received
18 August
1987
A method has been devised for determining the density of a fluid by measuring the velocity and amplitude of an ultrasonic pulse passed through it. The theory of the method is presented, together with the results of an experimental verification. Keywords: ultrasonic testing; ment; process control
density
measure-
Density measurement of liquids is most easily executed by sampling, i.e. by weighing a known volume. This process is sufficient for many purposes, but is difficult to automate and by its discontinuous nature does not lend itself to continuous monitoring. It is thus unsuited to process control. A survey of commercial process instrumentation indicates that the commonest method used for continuous measurement of density is resonant vibration. There are many variations on this theme, but they all make use of the fact that the resonant frequency of a system varies with its mass. The resonant frequency of some flexible member containing a volume of the process fluid is measured and from this the fluid density is calculated. There are two problems with the resonant vibration method: the instrument normally allows only a small flow and so has to use a bleed off from the main process flow; the method is insensitive to small changes in density. By extension of the well-known expression resonant frequency = (k/m)“2/27r (where k = stiffness, m = mass), the measured parameter (frequency) is proportional to only the square root of the parameter of interest (mass or density). Thus a small change in density will produce a very small shift in resonant frequency which is difficult to measure. An alternative to resonant vibration is the use of ultrasonics. It is well known that pulse velocity and attenuation are affected by the density of the medium through which an ultrasonic pulse is propagated, the relationship depending on the type of wave. The problem is that they are also affected by other factors such as temperature. To date no simple general purpose transducer has been developed to exploit the non-invasive nature of ultrasonics to measure density. 0041-624X/88/060356-02 @ 1988 Butterworth
356
$03.00 81 Co (Publishers)
Ltd
Ultrasonics 1988 Vol 26 November
Concept
An ideal ultrasonic density transducer for process control would consist of one or two probes set radially into the wall of the pipe carrying the process fluid. This would offer no flow restriction and would measure the density of the fluid overall, not just the portion bled off into a by-pass transducer. With two probes set diametrically opposite, one would act as the transmitter and the other the receiver. Alternatively, a single probe could serve both functions with the ultrasonic pulses being reflected off the back wall of the pipe. This ideal may be realized by making use of the fact that a wave meeting an interface between two different materials is partly reflected and partly transmitted through it. The proportion transmitted is dependent only on the acoustic impedance Z of the two materials, where acoustic impedance is the product of density p and pulse velocity c. The intensity at the receiver is thus the intensity at the transmitter, less the transmission losses at the two interfaces between the probes and the fluid, less any losses in the fluid itself. Neglecting the internal losses since these are not likely to change significantly for a given fluid, if two probes of known acoustic impedance are used then changes in received intensity must be due to changes in the acoustic impedance of the process fluid. And since pulse velocity c can be measured directly from the pulse propagation time (the distance between the probes being known), the density of the fluid is the only remaining variable. Theory
-7=-t-z2
I1
z3
Transmitter
where A = pulse amplitude and Z = acoustic impedance. A2 -=-
221
Al
z,
4 -=P=_
‘4,
+z2
A,=a
222
222
z,+z,
A,
A,
.. . A,=(Z, ... A =tz, 1
Zl
since Z, = Z,
+z,
4ctz,z, +z,y +
‘25
4az,z,
4
where Z, ( = Z,) is a constant for a given pair of probes. Consider two different fluids, a reference and an unknown, of acoustic impedance Z, and Z,, respectively. For a constant input pulse amplitude A, let the received
Research note pulse amplitude A, be A, and A,, respectively, then
(21 + ZRY JZl A
4crz,z,
R
+zx)2A
4aZ,Z,
assuming the attenuation yields a quadratic in Z, z,2+
(
Equipment
(2)
x
a does not change greatly this
2z,_(Z’~Z”)2~)z,+z:_o R x
(3)
which may be solved in the usual way to yield two values of Z, provided Z, is known (see Appendix). From Z, = c,p,, using the measured pulse velocity c,, density pX may be calculated. Alternatively, let Z, = Z, + 6Z and A, = A, + &I, then Equation (2) becomes (ZI + ZR)2 A =(ZI+ZR+fiZ)2(A Z,+6z ZR R
+6A) R
neglecting small terms 6Z2 and 6Z6A, this reduces to 6Z
-_=
(4)
zR
Thus, change in acoustic impedance is directly proportional to measured change in pulse amplitude Z,=Z,+6Z
:. px =
z,+6z
(5)
and test methods
The ultrasonic pulser/detector used was a Sonatest UFS 7A. The probes were Sonatest SLlH 5-10 5 MHz immersion probes (unfocussed). The probes were set up in a tank of test fluid at a spacing of 170 mm. The pulse amplitude was measured as the height of the largest peak of the rectified signal. The pulse propagation time was measured from the detector trigger point to the received pulse break point. Conclusions The initial test of the theory outlined above gives good agreement between the ultrasonic measurement of a test fluid density and the direct measurement by weighing a measured volume. Determining either the change in acoustic impedance of the fluid or its absolute value gave a calculated density with less than 2% deviation from the true value. Of the two methods presented, the more useful is the determination of the change in acoustic impedance because it is more easily implemented on a process control computer or programmable logic controller (PLC). Calculation of absolute impedance requires the solution of a quadratic which, while not in itself difficult, contains the inherent ambiguity of two solutions, only one of which is required. Change in impedance, on the other hand, is directly proportional to change in received pulse amplitude from which density is easily calculated. Appendix
Testing The theory was tested by measuring the density of a solution of salt water (of a different concentration to that used to determine the acoustic impedance of the probes). The density obtained ultrasonically was compared with the true value obtained by weighing a known quantity of the liquid. The reference fluid used was tap water where pR = 991kgm-3,cR=1510ms-‘soZR=1.50x106kgm-2s-’. For the test fluid, c, = 1770 m s-l, A, = 9.6 mV, A, = 8.1 mV, and pX (measured directly by weighing) = 1174 kg rnm3. Solving Equation (3) gives two values for Z, of 170 x lo3 or 2.1 x lo6 kg m-2 s-l. Taking the larger value gives pX = 1200 kg m-3, a discrepancy of 2%. Alternatively, Equation (4) gives change in acoustic impedance 6Z = 550 x lo3 kg m-’ s-‘. From Equation (5), pX = 1150 kg m - 3, a discrepancy of 2%.
To determine acoustic impedance of probes. Using two reference fluids of known acoustic impedance Z, and Z,, respectively, Equation (2) becomes (Zl
+
Za)” p1
4crz,z,
A
a
+zblZA 4az,z,
b
This may be rearranged to form a quadratic in Z,
Using tap water for fluid a and salt water for fluid b c, = 1510 m s-l, p,=991kgm-3,Z,=1.50x106kgm-2s-’
A, - = 0.865 A, There is only one positive root to the quadratic: Z, = 600 x lo3 kg mm2 s-l for the probes used.
Ultrasonics 1988 Vol 26 November
357